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A unifrom metallic ring of mass m, rad...

A unifrom metallic ring of mass `m`, radisus `R`, cross sectional area `'a'` and young'/s modulus `Y` kis kept on a smooth cone of radius `2R` and semivertex angle `45^(@)` as shown. [Assume that extension in the ring is small]

A

The tension in the ring will be same through out

B

The tension in the ring will be independent of radius of ring.

C

The extension in the ring will be `(mgR)/(aY)`

D

Elastic potential energy should in the ring will be `(m^(2) g^(2) R)/(8pi Ya)`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
`2T sin ((d theta)/(2)) = (N)/(sqrt(2)) = dm xx g`
or `T d theta = (M)/(2pi R) (R d theta)g` or `T = (Mg)/(2pi)`
Elonagation `= (T)/(aY) xx 2pi R = (MgR)/(aY)`
Energy `= (1)/(2) xx "stress" xx "strain" xx "volume" = (m^(2) g^(2))/(8pi^(2) a^(2) Y)`
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Knowledge Check

  • A ring of radius R is made of a thin wire of material of density rho , having cross-section area a and Young's modulus y. The ring rotates about an axis perpendicular to its plane and through its centre. Angular frequency of rotation is omega . The tension in the ring will be

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    D
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  • If a metal wire of length L, having area of cross-section A and young' s modulus Y . Behave as a spring of spring constant K. The value of K is

    A
    `(YA)/(L)`
    B
    `(YA)/(2L)`
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    `(2YA)/(L)`
    D
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    C
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    D
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